Plasma and trap-based techniques for science with antimatter J. Fajans1,a and C. M. Surko2,b 1 Physics Department, University of California Berkeley 2 Physics Department, University of California San Diego

ABSTRACT

Positrons (i.e., antielectrons) find use in a wide variety of applications, and antiprotons are required for the formation and study of antihydrogen. Available sources of these antiparticles are relatively weak. To optimize their use, most applications require that the antiparticles be accumulated into carefully prepared plasmas. We present an overview of the techniques that have been developed to efficiently accumulate low energy antiparticles and create specially tailored antiparticle plasmas. Techniques are also described to create tailored antiparticle beams. Many of these techniques are based on methods first developed by the nonneutral plasma community using electron plasmas for increased data rate. They have enabled the creation and trapping of antihydrogen, they have been critical to studies of positron and positronium interactions with matter, including advanced techniques to characterize materials and material surfaces; and they have led to the creation and study of the positronium molecule. Rather than attempting to be comprehensive, we focus on techniques that have proven most useful, applications where there has been significant, recent progress, and areas that hold promise for future advances. Examples of the latter include ever more precise comparisons of the properties of antihydrogen and hydrogen, tests of gravity using antihydrogen and positronium atoms, and efforts to create and study phases of the many-electron, many-positron system.

currents, only pico-Coulombs at sub-pico-amp currents are I. INTRODUCTION available in the case of positrons. Antiprotons for low-energy research with antimatter are available only at the Antiproton In the past few decades, the use of antimatter for scientific and Decelerator (AD) [16] at CERN in Geneva, Switzerland. Once technological purposes has become increasingly important. degraded to below 5 kV, bunches of only ~ 105 antiprotons are Positrons are used to characterize materials and material surfaces delivered by the AD, at a rate of one bunch every two minutes. [1], and for positron emission tomography (PET) which is used in The new upgrade to the AD, ELENA [17], is expected to deliver drug design and to study metabolic processes [2]. Scientific 10–100 times more useable antiprotons. applications include tests of quantum electrodynamics (QED), creation of exotic species such as positronium (Ps) and the Some applications demand tailored antiparticle beams. + - + - positronium molecule (e e e e , symbol Ps2) [3, 4], and Depending on the application, one might want fine lateral understanding fundamental positron interactions with ordinary focusing, high areal densities, low-energy beams, nearly matter including atoms and molecules [5, 6]. One of the newest monoenergetic beams, or short temporal pulses. Alternatively, developments is the ability to create high-quality beams of one might want to deliver intense bursts of large numbers of positronium atoms for precision measurements and for antiparticles. fundamental physics tests, such as the gravitational attraction of antimatter to our (matter) earth [7, 8]. Other applications work best with confined antiparticles. Because antiparticles suffer annihilation when they come in Antiprotons play a central role in the formation and study of contact with matter, they must be confined in vacuum, typically antihydrogen (the bound state of the antiproton and the positron in an electromagnetic trap. The antiparticles form a charged and the simplest stable antiatom). Antihydrogen is being used to cloud which is often in the plasma state. The focus of this article test the CPT theorem (i.e., the predicted invariance of relativistic is to describe the techniques required to accumulate antiparticles quantum field theories under charge conjugation, parity inversion and manipulate the resulting plasmas, tailored for specific and time reversal) and the gravitational attraction of antimatter to applications. The techniques described here rely heavily on matter. Results have been obtained for the 1S-2S transition [9], research in plasma and beam physics [15]. In particular, many and the hyperfine transition [10], which, by an absolute energy useful processes are extensions of techniques developed to tailor metric [11], are some of the most precise tests to-date of the CPT more conventional single-component plasmas (i.e., plasmas theorem. Crude measurements of the interaction of antihydrogen composed of electrons or ions) and mixed-species nonneutral with the earth’s gravitational field have also been performed [12]. plasmas. CPT tests such as a comparison of the proton/antiproton magnetic moment and mass have also been performed with isolated II. ANTIMATTER PLASMAS IN TRAPS antiprotons [13, 14]. These tests have attracted much attention, both in the physics community and with the lay public. A. Penning-Malmberg traps

Sources of antiparticles are relatively weak. Positrons can be A wide variety of electromagnetic traps have been used to confine obtained from a variety of radioisotopes, nuclear reactors, and positrons, including Penning traps, magnetic mirrors and levitated linear electron accelerators (LINACS) [15]. However, while one magnetic dipoles [18-22]. For long-time confinement of large can easily obtain many Coulombs of electrons at amp-strength numbers of positrons or antiprotons, the method of choice is some a [email protected] b [email protected]

1 variant of the Penning-Malmberg (PM) trap [23]. As shown in asymmetries [28]. Recent evidence suggests that colloidal- Fig. 1, PM traps use a uniform magnetic field for radial graphite-coated electrodes are superior to electroplated gold in confinement and an electrostatic potential well in the magnetic minimizing patch asymmetries [29]. field direction for axial confinement. These traps are used to confine gases or plasmas whose constituents are all of the same In practice, plasma confinement times in PM traps range from charge sign, though in antihydrogen synthesis, two adjacent, milliseconds to hours and scale approximately as [27]. There 1 oppositely charged plasmas are merged. As pointed out by is evidence that confinement is superior in multi-ring2 PM traps O’Neil, for a cold, magnetized plasma consisting of particles with [30], which utilize many short electrodes extending𝐵𝐵 over the a single sign of charge, the canonical angular momentum in a PM length of the plasma, rather than one long electrode, as depicted trap can be approximated as in Fig. 1. These short electrodes can be used to generate a near- harmonic potential. Investigation of the possibly better , (1) performance of such multi-ring traps is a fruitful area for further 𝑒𝑒𝑒𝑒 research. 2 𝑧𝑧 2 𝑗𝑗 𝑗𝑗 where z is the direction𝐿𝐿 ≈ of∑ the𝑟𝑟 magnetic field B, and is the radial B. Ultra-long-time confinement position of particle j with charge e (SI units) [24]. If there are no 𝑗𝑗 torques on the plasma, the angular momentum is constant𝑟𝑟 and the If long-time confinement is needed, antiparticles can be plasma cannot expand. Thus, confinement is nominally perfect, transferred to an ultra-high vacuum (UHV) PM trap where and the plasma can reach an equilibrium state [25]. annihilation losses are minimized (cf. Fig. 2) [31]. Transfer efficiencies can be in excess of 90 %, but can also be lower depending upon the specific circumstances. Antimatter can be routinely confined in such traps for days, and in exceptional cases, years [13, 32], using traps mostly or entirely enclosed by surfaces at 4.2 K. Pressures below 10-14 Torr are readily obtained in such cryogenic traps, and can go as low as ~10 Torr [13, 32]. When necessary, plasma expansion can −be18 minimized or eliminated by applying rotating electric fields [i.e., the “rotating Fig. 1. Schematic diagram of a Penning-Malmberg trap for the wall” (RW) technique [33]]. The RW technique and long confinement of plasmas consisting of particles of a single sign of confinement also require good particle cooling, which can be charge, here biased for positive charges. Typical electrode radii provided by cyclotron radiation in strong (e.g., tesla-strength) and lengths are several centimeters. The “parallel” direction z is magnetic fields. We defer further discussion of the performance defined to be aligned with the trap and magnetic axes, and and limits of UHV traps to the later sections on cyclotron cooling “perpendicular” refers to the orthogonal directions. and the RW technique.

A plasma in a PM trap produces a strong radial electric field. This C. Buffer-gas PM traps field results in an E x B drift in the azimuthal direction, which causes the plasma to spin about the magnetic axis. With good Sources of positrons typically produce particles with energies of confinement, the shears in the plasma damp out, and the plasma kilo-electron volts or higher. There is not yet an efficient way to rotates as a rigid rotor at frequency trap particles at these energies, and so various materials (“moderators”) are used to slow them to electron volt energies [1, = , (2) 15, 34-36], whereupon they can be trapped in a buffer-gas trap 𝑒𝑒𝑒𝑒 (BGT). The BGT (cf. Fig. 2) is a modified PM trap that employs 𝑓𝑓𝐸𝐸 4𝜋𝜋𝜀𝜀0𝐵𝐵 where is the plasma density [26] and is the permittivity of a stepped potential well in the B direction and corresponding free space. Depending upon the application, PM traps can operate regions (stages) of varying gas pressure. The highest-pressure at a variety𝑛𝑛 of magnetic fields (e.g., 0.01–𝜀𝜀70 tesla). As discussed in region (stage I) is used to trap the particles by electronic excitation the next section, particle cooling is frequently necessary. At high of a molecule (N2 is the molecule of choice) in one transit through (e.g., tesla-strength) magnetic fields, naturally occurring the trap. Subsequent collisions act to move the particles to stages cyclotron radiation can fill this role, while at low B, other of lower potential and gas pressure, where annihilation is slower techniques, such as collisions with a molecular gas, are used. (e.g., annihilation times ~ 100 s). Buffer-gas traps using solid Ne moderators can have as high as 30% trapping efficiency [34]. Plasma expansion and losses in PM traps have been extensively investigated [15, 24, 27]. They are believed to be due to torques The operating cycle of the BGT will depend upon the application. induced by azimuthal asymmetries. The transport induced by For energy-resolved scattering and annihilation experiments, one these torques cannot yet be predicted by theory for a particular desires to avoid space charge effects. Trap operation is typically device. Thus, when constructing a trap, one endeavors to a few Hz, with microsecond pulses of 103 – 104 positrons. In other minimize magnetic and electrostatic asymmetries. Even with a applications, one may want large bursts of positrons in which case perfectly symmetric trap, patch potentials can produce deleterious accumulation (and hence cycle) times can be of order 100 s.

1 Usually, but not always, the charge clouds are in the plasma = ( / ) / is the Debye length, is the permittivity of regime, which is defined by < and ( ) > 1, where free space, is2 the1 2plasma temperature, L is the characteristic 𝐷𝐷 0 0 3 𝜆𝜆dimension𝜀𝜀 𝑇𝑇 of𝑛𝑛 𝑒𝑒the plasma, and is the plasma𝜀𝜀 density. 𝜆𝜆𝐷𝐷 𝐿𝐿 𝑛𝑛 𝜆𝜆𝐷𝐷 𝑇𝑇 𝑛𝑛 2 Discussed below are techniques developed to “bunch” the plasma profile and aspect ratio can also be determined by positron bursts into nanosecond pulses. measuring the plasma axial bounce and breathing mode frequencies [41, 42]. While often useful, the reconstruction of the Even in the low-pressure regions of BGT traps annihilation can plasma parameters is hindered by wall effects, and, for needle- be problematic. When longer time confinement times are needed, like (high aspect ratio) plasmas, by a numeric instability in the the positrons can be transferred to an UHV trap such as those formulas for the mode frequencies. discussed above [31]. Temperature. The parallel plasma temperature can be measured by lowering the barrier that confines the plasma slowly compared to the bounce time of the plasma particles. The most energetic plasma particles will escape first and can be counted with a Faraday cup or scintillators. The temperature can then be determined from the count vs. confinement voltage profile [43]. Only particles escaping from within a few Debye lengths of the plasma center contain temperature information. This makes the diagnostic difficult to operate at low temperatures (sub 100K), and an MCP is often necessary to amplify the signal from these few escaping particles. The temperature can be measured from Fig. 2. Schematic diagram of a three-stage buffer-gas positron just one plasma sample. To-date, this method of measuring the trap and an adjacent high-magnetic-field UHV trap (HFT) [31]. temperature has been most generally useful in antihydrogen In the BGT, each of the latter two stages are at successively lower trapping. However, there are other methods of measuring the buffer-gas pressures and lower electrical potentials. temperature, several of which are described below. Of these, the modes diagnostics has been the most useful. III. PLASMA DIAGNOSTICS The perpendicular plasma temperature can be measured by using Diagnostics measuring the plasma density, radius, length, and a magnetic gradient field to convert perpendicular to parallel temperature have played a key role in the development of the energy in conjunction with an electrostatic energy barrier [44, physics of antimatter plasmas. Experience has shown that the 45]. This technique has the advantage that it measures the bulk progress of underdiagnosed experiments has suffered. Many of distribution, rather than the Maxwellian tail distribution as is these diagnostics were first developed by the nonneutral plasma measured by the parallel temperature diagnostic described community, but the unique conditions of antimatter experiments immediately above. However, the technique requires a gradient- (sometimes tenuous plasmas, cryogenic traps with poor access, producing coil as well as multiple plasma samples, and the ultralow plasma temperatures) have made applying them difficult. samples must be nearly identical. To our knowledge, the technique has not been implemented for antimatter plasmas. Total particle number. Because antimatter plasmas typically contain only one sign of charge, the total charge can be detected Plasma temperatures can also be measured by systematic trends by destructively dumping the plasma onto a Faraday cup, or if the in the bounce and breathing mode frequencies [46-48]. While this plasma is tenuous, a microchannel plate (MCP). Alternatively, diagnostic has the advantage that it is nondestructive, it should be the charge can be counted by detecting the annihilation emphasized that this is a relative temperature diagnostic and does byproducts (gamma rays for positrons, pions for antiprotons) on not yield absolute temperatures. Moreover, the numeric particle detectors (commonly scintillators or Si-based devices). instabilities and wall effects previously mentioned hinder its Calibration of annihilation-based diagnostics is complicated by applicability. solid angle, scattering, and absorption issues. For a single component plasma, one can also extract small pulses Plasma density profile and aspect ratio. The areal plasma of charge by lowering an end gate (i.e., as with the velocity density (the density projected onto the transverse plane, measurement described in the previous paragraph). The charge, [ ] typically in units of cm ) can be determined by destructively which will come from the region near the axis, has a Gaussian dumping the plasma onto− 2a phosphor screen and imaging the radial distribution with a 1/e width of two Debye lengths [49]. If resultant light with a CCD camera. For a recent study of the other measures of the density are available, the width of the pulse difference in detection characteristics of phosphor screens for provides a measurement of the plasma temperature. electrons and positrons, see Ref. [37]. Often, an MCP is used to brightness-enhance the image [38, 39]. Typically, the type of Finally, the temperature can be determined by measuring the particle being detected is known beforehand. If not, there are thermal fluctuations in the naturally excited plasma-mode other ways to distinguish them. For example, antiprotons are amplitudes [50]. Unfortunately, this otherwise advantageous approximately a factor of 100 brighter than leptons on an MCP, technique requires a true thermal equilibrium (i.e., without and antiparticles will have characteristic annihilation products extrinsic noise) and good signal-to-noise. Consequently, it is that can be detected separately. difficult to apply at low temperatures (< 300K) or in a noisy environment.

The plasma aspect ratio (length to radius), and radial density profile ( ) [cm ] can be determined numerically from the areal density, the total −charge,3 and the confinement geometry [40]. The 𝑛𝑛 𝑟𝑟

3 IV. PLASMA MANIPULATION TECHNIQUES Cyclotron cooling. In a magnetic field, the cyclotron orbits of the A. Plasma cooling and temperature control particles result in the emission of radiation. This can be an efficient cooling mechanism for the perpendicular degrees of For most applications, good particle cooling is either desirable or freedom of electrons and positrons [53, 54]. Except under necessary to avoid deleterious effects (e.g., ionization and/or extreme conditions of high fields and low temperatures [55], positronium formation on background gas, and evaporative collisions thermalize the parallel and perpendicular energies at a particle loss). Cooling methods include using a buffer gas and rate much faster than the cooling itself. Including this cyclotron radiation, as well as sympathetic cooling via laser- thermalization, the free-space cooling rate (in units of s-1) is cooled ions and adiabatic and evaporative cooling. Ω Γ = = 0.26 2 2 , (3) Buffer gas cooling. Cooling of positrons using a molecular gas is 1 𝑑𝑑𝑑𝑑 2𝑒𝑒 𝑐𝑐 𝐵𝐵 2 3 now a well-established technique [15, 51, 52], and it is central to 𝑐𝑐 𝑇𝑇 𝑑𝑑𝑑𝑑 9𝜋𝜋𝜀𝜀0𝑚𝑚𝑐𝑐 ≈ �1𝑇𝑇� the operation of the buffer-gas positron trap. Where possible where is the plasma temperature, = / is the cyclotron (initial trapping in a BGT being an exception), one tries to avoid frequency, m is the particle mass, and is the speed of light. 𝑐𝑐 energy loss by electronic excitation, since this occurs close in Cyclotron𝑇𝑇 cooling has been exploitedΩ extensively𝑒𝑒𝑒𝑒 𝑚𝑚 at tesla-strength energy to positronium-atom formation which is a virulent magnetic fields. While generally not as fast𝑐𝑐 as buffer-gas cooling, positron-annihilation loss process. Thus, one relies on molecular it is compatible with UHV vacuum environments and thus avoids collisions and the associated excitation of vibrations and rotations the use of a buffer gas and the associated annihilation loss. for cooling (i.e., below the threshold for positronium atom formation). As long as the positrons do not form positron- Recently, a resonant cavity was used to enhance the cyclotron molecule bound states (which are absent for many small cooling rate (cf. Figs. 4 and 5) [56]. As in the Purcell effect, the molecules), annihilation (a key limitation of this technique) is cavity enhances the cyclotron rate [57]. Electron plasmas have relatively benign. Depending upon the choice of molecule, been cooled to 10 K with a rate 100 times faster than the cooling times from energies of ~ 1 eV to 25 meV (11,600 to 300 spontaneous rate given by Eq. (3). Fast cooling has been observed K) range from < 10 ms to 1 s at gas pressures ~ 10-6 torr [52]. in fields as low as 0.15T, where the free-space cyclotron cooling rate is very small. While there is some limitation on the number Molecular nitrogen N2 is used in BGT for the initial trapping of particles that can be cooled in this manner, resonant cavity (energy loss ~ 10 eV/collision), since the cross section for cooling offers considerable potential, particularly when one wants electronic excitation near the threshold is large at energies before to operate in UHV conditions and/or at low magnetic fields. positronium formation dominates. The N2 is frequently augmented by CF4 or SF6 for more rapid vibrational cooling to Sympathetic cooling on electrons. A key advance in antimatter lower temperatures. The rates for cooling to 300 K due to physics was the development of techniques to trap and cool vibrational and rotational collisions are compared for three energetic antiprotons. Antiprotons from CERN’s LEAR (and molecules in Fig. 3 [52]. At 10-6 Torr of these gases, positron later the AD) facility can be slowed by a degrader. About 0.5% of annihilation times are ~ 102 s. A recently developed cryogenic the antiprotons in the 5.3 MeV AD beam can be slowed to below BGT operating at 50 K used the CO molecule [29], which has a 5 keV. These antiprotons can then be “barn-door trapped” with an permanent dipole moment and hence enhanced rotational energy efficiency approaching 100% by the application of a fast-rising loss. The CO has a sufficiently high vapor pressure so as to not electrode potential, resulting in a cloud of 0 − 5keV antiprotons freeze out at 50 K. Buffer gas cooling to temperatures as low as in a PM trap [58]. The antiprotons can then be cooled to ~5 meV 20 K appears to be possible with H2, but cooling will be slow (i.e., temperatures by collisions with cyclotron-cooled electrons [59]. comparable to N2). Note that because of baryon number conservation, antiprotons do not annihilate on electrons.

Fig. 4. (a) Electrodes of a PM trap designed to exploit resonant- cavity cyclotron cooling in resonant Cavity 2. Cavities 1 and 3 act as waveguides beyond cutoff. (b) the simulated electric field

intensity for the TE111 mode in Cavity 2 [56]. Fig. 3. Positron cooling on molecular vibrations and rotations for

() CF4, (▲) CO, and (■) N2 gases at 300 K (horizontal line) [52]. The data are normalized to 1 μtorr and shifted to coincide at t = 0 s; the dashed lines show an exponential fit for each case. Inset shows CF4 in more detail. The corresponding cooling times to 1/e are 4.8, 130, and 1,500 ms/µtorr for CF4, CO, and N2.

4 component plasmas, charged gases in the single particle regime, and cold, high density ion crystals [33, 65-70]. To use this technique, phased electrical signals at some frequency are used to drive azimuthally segmented sectors of an electrode surrounding an axial portion of the plasma. The electric𝑓𝑓𝑅𝑅𝑅𝑅 field induces a dipole moment, resulting in a torque. This torque increases the rotation frequency of the plasma and thus acts to increase the density as per Eq. (2) (see Fig. 8). The RW technique can be used to increase the plasma density and/or to achieve long Fig. 5. Measured temperatures of electron plasmas initially at term particle confinement (e.g., days, weeks or longer). It has 26,000 K and cooled for 8 s at the indicated magnetic field values proven useful in both BG and UHV traps [15, 69, 70]. using the apparatus in Fig. 4. The dips occur upon excitation of TE11X modes [56].

Sympathetic cooling using laser-cooled ions. Small numbers of positrons (~ 1000) have been sympathetically cooled to < 5 K when they were co-loaded in a PM trap with a larger number (~105) of laser-cooled Be+ ions. However, deleterious centrifugal𝑇𝑇 separation was observed [60]. Further work is necessary to determine the extent to which centrifugal separation is an intrinsic limitation, and also to determine if a large number of positrons (≥ 106) can be cooled with a smaller number of ions (e.g., ~ 105) [61].

Adiabatic expansion. Adiabatic expansion can be used to cool nonneutral plasmas [45] to temperatures below 10K. In this process, the electrostatic confining potential well is expanded FIG. 6. (a) Six steps of evaporative cooling of antiprotons, axially. By conservation of the bounce adiabatic invariant, the resulting in a temperature decrease from 1,000 K to 9 K (■). The plasma will cool. For best results, the well must be expanded temperature vs. the on-axis well depth is compared with a model slowly compared to the particle bounce time, since this preserves calculation (solid line). The initial number of antiprotons was the adiabatic nature of the expansion. While the plasma only approximately 45,000 at an on-axis well depth of 1.5 eV. directly cools in the axial direction, Coulomb collisions Approximately 6 % of the particles remain at the final thermalize the plasma in all directions. temperature of 9 K. See Ref. [63] for details.

Evaporative cooling. Nonneutral plasmas can also be cooled by The torque due to the RW fields does work on the plasma and evaporative cooling, in which the electrostatic confining well hence produces heating [33]. Thus, RW compression requires a barrier is lowered so that the hottest plasma particles escape. The plasma cooling mechanism. This cooling can be provided by the remaining plasma then re-thermalizes on the collision time scale. background gas in BG traps, by cyclotron cooling in UHV traps, An example of the use of this method to cool antiprotons is shown or laser cooling using co-loaded ions. For antiprotons, in Fig. 6. sympathetic cooling on co-trapped cyclotron-cooled electrons can be used [71]. One group, however, has reported RW Both adiabatic expansion and evaporative cooling have proven compression without an obvious cooling mechanism [72]. useful and important in antimatter physics experiments (e.g., see Refs. [62-64] for cooling both positrons and antiprotons. Expansion cooling retains all of the particles, which is advantageous. It does, however, expand the plasma axially, which lowers the plasma density. Evaporative cooling necessarily involves loss of particles, though with care, this loss can be minimized. Further, angular momentum conservation requires that the plasma expand radially [24], which also lowers the plasma density. Fig. 7. Apparatus for RW compression of single component, negatively charged plasmas. The areal density profile is measured B. Plasma density control—the “rotating wall technique” by accelerating the particles onto a phosphor screen and measuring the resulting light, as discussed in Section III. If there are no torques on a plasma in a PM trap, angular momentum is conserved and there is no net expansion. However, realistic plasma traps always have asymmetries which act to Particle heating is reduced when the asymmetry-induced expand the plasma. If one injects angular momentum by transport is minimized, and this is desirable. For a single deliberately applying a torque, one can compress the plasma as component plasma in a PM trap with good confinement, the required by Eq. (1) and counteract the intrinsic expansion. Such plasma density n approaches a constant, independent of the radial torques can be applied by the “rotating wall” (RW) technique position in the plasma. As illustrated in Fig. 9, when the applied illustrated in Fig. 7. It has been used to compress single- frequency > , the plasma can be made to spin up until the

𝑓𝑓𝑅𝑅𝑅𝑅 𝑓𝑓𝐸𝐸 5 two frequencies are approximately equal, namely (the The parameters of plasmas loaded into PM traps can vary so-called “strong drive regime” of RW compression) [33, 73]. substantially from loading to loading. Some of this variation Experience has shown, however, that PM traps 𝑓𝑓with𝐸𝐸 ≈ relatively𝑓𝑓𝑅𝑅𝑅𝑅 comes from the particle source itself: for positron sources, for good confinement are required in order to be able to operate in instance, due to the variations in pumping, the quality and age of this strong drive regime. the moderator, and other factors. In some experiments, the number of trapped positrons can easily vary by a factor of two. The Brillouin density limit, = /(2 ), where is the Other variations can come from the transport of particles from permeability of free space, is the maximum2 plasma2 density that low to high magnetic field, where magnetic mirroring can play a can be confined in a magnetic𝑛𝑛𝐵𝐵 field𝐵𝐵 B [74]𝜇𝜇0𝑚𝑚𝑐𝑐. As shown in𝜇𝜇 0Fig. 9, significant role. Mirroring can be reduced by transferring the for plasmas in PM traps using buffer gas cooling, densities of 17% particles at an axial energy much greater than the plasma of have been achieved. That this is not 100 % of can likely temperature; however, as discussed below, this can introduce be understood as limited by molecular collisions in the relatively other problems. 𝐵𝐵 𝐵𝐵 strong𝑛𝑛 radial electric fields near [75]. In contrast,𝑛𝑛 while higher absolute densities have been achieved in cyclotron-cooled In some applications, such as the trapping of antihydrogen, the plasmas in high-field UHV traps,𝑛𝑛𝐵𝐵 the fraction of the Brillouin reproducibility of the plasma loading is critical. Reproducibility limit achieved is much smaller (e.g., / 10 ). The can be dramatically improved by simultaneously employing relatively poor performance in this regime is not understood−3 and strong-drive RW fields (SDR) (which sets the plasma density) is a subject of ongoing research. 𝑛𝑛 𝑛𝑛𝐵𝐵 ≤ and evaporative cooling (EVC) (which sets the plasma on-axis potential). So long as the temperature is low, setting the density and the on-axis potential fully specifies the remaining plasma parameters, including the plasma radius and total charge. An example of this procedure, called SDREVC [62], is shown in Fig. 10. The stability engendered by SDREVC has led to more than an order of magnitude increase in the formation rate of trappable antihydrogen.

Fig. 8. Rotating wall compression of an electron plasma starting at time = 0 [76]. Note the log density scale. The constant density profiles at t = 0 and 10 s are characteristic of rigid-rotor rotational𝑡𝑡 motion [i.e., as described by Eq. (2)].

Fig. 10. Stability of the electron and positron plasmas (the former for sympathetic cooling of the antiprotons) used to create antihydrogen atoms before and after plasma tailoring by radial compression and evaporative cooling (SDREVC) [62].

D. Plasma purity control for antihydrogen formation

While some plasma processes used to form antihydrogen require or tolerate multispecies plasmas, many require that the plasmas be pure. Some techniques to purify the plasmas are given below.

Fig. 9. Change in density of a positron plasma as a function of Removal of cooling electrons. Antiprotons are initially captured applied RW frequency when a constant frequency is applied [15]. from the AD by sympathetic cooling on electrons. These The solid line corresponds to = , characteristic of the electrons must be removed from the mixed antiproton/electron strong drive regime. For this experiment, B = 0.04 T, and the plasma before the antiprotons can be moved substantial distances maximum density achieved is 17%𝑓𝑓𝐸𝐸 of 𝑓𝑓the𝑅𝑅𝑅𝑅 Brillouin density limit. (e.g., to another trap). Once moved, the antiprotons are frequently The sharp drops in density at specific frequencies are due to static remixed with new electrons to re-cool them. These electrons must asymmetries that couple to low-order plasma modes and act as a be subsequently removed before the antiprotons are further drag on the plasma. processed to make antihydrogen. The electrons are usually removed by momentarily lowering the electrostatic confinement well trapping the mixed plasmas. Because the electrons are much C. Combined techniques to provide unprecedented plasma lighter than the antiprotons, they will escape the trap before the reproducibility antiprotons respond significantly. This process, sometimes called “e-kicking,” is somewhat delicate. Lowering the barrier too much

6 or for too long a time, heats or even loses the antiprotons, while further processed. This can be accomplished by a modified e- lowering the barrier too little or for too short a time, does not kicking process, in which the ejected, now pure, positrons are remove all the electrons. then re-caught in a potential well downstream, or by driving the ions out of the positron plasma with a frequency resonant with the To obtain pure, cold, antiprotons plasmas, it is often necessary to ion bounce frequency. When done carefully, few positrons are perform several cycles of ever deeper, albeit incompletely lost by these cleaning operations. effective e-kicks. Between each cycle, the antiprotons are E. Autoresonance. sympathetically re-cooled on the ever-diminishing number of electrons. E-kicking also expands the remaining plasma, Under certain circumstances, a nonlinear oscillator can be made counteracting sympathetically cooled antiproton compression. to phase lock to a drive signal if the drive frequency is slowly Thus, it is frequently necessary to do compression in several swept through the linear (low amplitude) resonant frequency of stages, separated by the partial e-kicks. Consequently, the the system [78]. This phenomenon, called autoresonance, has optimal tuning of this process is subtle [77], but when well-tuned, proven useful to coherently manipulate plasmas in PM traps. An few antiprotons are lost. example is shown in Fig. 11 where the longitudinal motion of an antiproton cloud in a PM trap has been excited and the cloud Positron cleaning. When positrons or other particles are released at various mean energies set by the end-gate potential transported long distances and/or into higher field regions, they [79]. In another application, development of a practical multicell are often transported at axial energies well above the initial positron trap for large numbers of positrons [80, 81], an electron plasma temperature. For example, a 50 eV transport energy is plasma was moved across the magnetic field by autoresonant often used. This energy is greater than the ionization and excitation of the diocotron mode (i.e., the bulk rotation of the positronium formation thresholds for background neutrals, and so plasma around the trap axis caused by the plasmas interaction the particles can become contaminated with background ions. with its image) [74]. This is particularly troublesome for positrons, because the background ions are typically positively charged, and are hence The combination of trapping and plasma manipulation techniques confined by the same electrostatic well as used to confine the has established the ability to create a wide variety of trapped positrons. These ions can cause fast expansion and plasma antimatter plasmas. Table I gives some examples. heating, and so they need to be removed before the positrons are

Table I. Examples of operating parameters for antimatter plasmas in PM traps, the plasma length and radius, Lp and rp, temperature and density, T and n, space charge potential, Vs, and the confinement time τc. Positrons: in gas-cooled traps: UCSD – three-stage BGT, UCR – 2-stage BGT, FPSI – First Point Scientific BGT and accumulator; and in cyclotron- cooled traps: the ALPHA [82], ATHENA [83] and ATRAP [84] collaborations at CERN. Antiprotons: the ALPHA [82], ATRAP [64], and AEgIS [77] collaborations at CERN.

Device B Lp rp T n Nmax Vs c (T) (cm) (mm) (eV) (cm)-3 (V) (s) Positrons 𝟖𝟖 𝟕𝟕 𝝉𝝉 UCSD 0.1 10 6 0.03 𝟏𝟏𝟏𝟏0.02 𝟏𝟏𝟏𝟏30 15 300 UCR 0.09 1 0.5 0.03 1 0.1 0.01 1 FPSI 0.04 10 0.5 0.05 12 10 ~10 ~1000 ALPHA† 1 1 0.7 0.001 1 3 0.2 ATHENA† 3 26 120 ~9000 ATRAP 1 400 530* ~14400 Antiprotons ALPHA† 1 1 1 0.0006 0.01 0.005 0.02 ATRAP 3.7 0.0003 0.3 AEgIS 4.46 0.17 0.2 0.007 † Not achieved simultaneously *Confinement voltage

V. TRAP-BASED ANTIPARTICLE BEAMS end gate barrier. Typically, the plasma is allowed to cool to the ambient gas temperature , in which case the achievable spread Different applications require different types of optimization of in total energy is approximately (3/2) kB . In more detail, the 𝑔𝑔 antiparticles beams generated from PM-trapped antiparticle beam energy distribution𝑇𝑇 can be described by an exponentially 𝑔𝑔 plasmas. Described here are some frequently used techniques. modified Gaussian (EMG) distribution𝑇𝑇 [85]. The energy distribution in the motion perpendicular to B is Maxwellian, but A. Narrow energy spreads the parallel energy depends on the dynamics of the expulsion of the particles from the PM trap and the shape of the confining Buffer-gas trap-based positron beams with narrow energy spreads potential well. Energy spreads of 40 meV FWHM have been have proven useful for studying positron scattering and achieved using a 300 K buffer gas and 7 meV with a gas at 50 K annihilation processes [5, 6]. A simple method to create a beam [15, 29]. is to trap and cool positrons in a PM trap and then carefully raise the bottom of the confining potential well to force them over an

7 B. Short temporal pulses difficult to do while simultaneously preserving beam quality. Techniques used to help maintain beam quality include For applications such as study of high-density gases of transmission through a small hole in a high-permeability plate and positronium atoms, one would like short temporal bursts of use of a specially designed grid made of a similar material [89, antiparticles. Examples include the creation of dense gases of 90]. If the objective is a beam with small transverse extent, this positronium atoms at material surfaces [86], matching lasers to can be preceded by center-line extraction. Following extraction collections of Ps atoms for precision spectroscopy, and preparing from the field, one can then focus the resulting particles long-lifetime, high-Rydberg-state Ps atoms for advanced Ps electrostatically (frequently using a remoderator [91]). This latter beams [8]. For example, the more focused in space and time the process can be repeated to further focus the beam, albeit with positron burst, the more efficiently it can be matched to laser some particle loss. Such narrow beams are of use, for example, in pulses for the manipulation of atoms (e.g., high-Rydberg Ps). applications such as positron microscopy. Temporal bunching technology is very highly developed due to its importance in tailoring electron beams, and so techniques are readily available for positron applications at the level of a few hundred picoseconds. One would like to achieve such short pulse durations for applications such as single-shot positron lifetime spectroscopy [87].

Fig. 12. Positron pulses with and without a harmonic buncher, showing time compression of a factor of approximately ten to < 2 ns [92].

Fig. 11. Autoresonant release of a cloud of antiprotons from a E. Spin-polarized positron beams potential well. The frequency is swept downward from the linear /2 value for this well with bounce frequency = 410 kHz. The For applications such as the creation and study of dense gases of open squares (right) denote the mean beam energy U of each Ps atoms, one would like to prepare the longer-lived spin S = 1 𝜔𝜔0 𝜋𝜋 distribution f(U) (left), plotted against the final drive frequency atoms. This has been done exploiting the fact that 22Na positron (dashed lines). See Ref. [79] for details. sources emit spin-polarized positrons (i.e., since the positrons are produced via the weak interactions). The approximately 30% One technique for temporal pulse compression is to confine the expected polarization was produced, and maintained even when plasma in a PM trap inside a stack of short cylindrical electrodes. the fast positrons from 22Na were moderated in energy using solid Shown in Fig. 12 are data using such a harmonic “buncher” to neon and trapped in a BGT, followed by density increase using a time-compress a pulse of positrons from a BGT accumulator. In RW and time-compressed using a harmonic buncher [93]. this technique, a positron plasma is confined in a multi-ring PM trap, the potential is quickly ramped up to a parabolic profile, with F. Trap-based positronium atom beams the minimum in the potential some distance downstream, thus producing a time focus at that location. Alternately, one can High quality Ps beams are important for characterizing materials produce short temporal pulses from an accelerator-based source as well as for tests of fundamental physics such as the [88]. gravitational attraction of matter and antimatter. This is an area which has seen considerable progress recently, and one that holds C. Beams with small transverse extent much promise for the future.

The RW technique can be used to increase plasma density. This, High-Rydberg-state Ps beams. The positronium atom is unstable in conjunction with carefully extracting positrons from the center to electron-positron annihilation. The lifetime depends upon the of the plasma (i.e., center-line extraction), can produce spin of the atom and the principle quantum number of the state. magnetically guided beams with small transverse spatial extent The lowest order annihilation process for ground-state Ps atoms (the limit being four Debye lengths) [49]. Such beams would aid with S = 1 is decay by the emission of three gamma rays with a in the use in positron microscopy to study material surfaces, as lifetime of 140 ns, while the S = 0 state decays by the emission of discussed further in the next section. two gamma rays with a lifetime of 120 ps [94]. These short lifetimes pose an important constraint on the creation and utility D. Electrostatic beams from trapped plasmas of Ps beams.

Techniques have been developed to extract positron beams from One recent approach, offering considerable promise to produce the magnetic field of a PM trap into a field free region. This is high quality Ps beams, exploits trap-based beam technology to

8 produce focused, time-compressed bursts of positrons. When describe the potential impact of tools currently under incident upon a specially chosen material surface, bursts of Ps development. atoms are produced that can then be matched to laser pulses to produce high-Rydberg-state Ps atoms [95]. In these atoms, the A. Formation, trapping and study of antihydrogen overlap of the positron and electron wave functions is relatively small, resulting in much longer lifetimes (e.g., lifetime ≥ 100 µs As mentioned above, an exciting area of science with antimatter for the n = 31 state). is the creation of antihydrogen atoms and precision tests of their properties compared with those of hydrogen. These activities are If these Rydberg atoms are made in a strong electric field (so- the focus of work by several world-wide collaborations at called Stark states) [8], they can have large permanent dipole CERN’s AD facility. Antihydrogen trap depths are less than 1 K. moments. They can then be manipulated (guided, focused) by Consequently, antihydrogen experiments must be done with suitably arranged regions of varying electric field. The schematic particles at very low particle energies. Plasma manipulation and diagram of a recent experiment is shown in Fig. 13. Typical Ps beam formation techniques have played a critical role in energies are a few tenths of an eV. Potentially, this technique is maximizing the efficiency of antihydrogen formation and an alternative method to form antihydrogen (ie., by the process of trapping. Important procedures include efficient antiparticle charge exchange of Rydberg Ps atoms with antiprotons) [96, 97] trapping, density and temperature control, and tailored mixing of and long-lived, high quality Ps beams for antimatter gravity positrons and antiprotons. (see Refs. [62, 100-102]). A recent studies [8]. success of this strategy is the newly developed SDREVC technique (cf. Sec. IV. C and Fig. 10) to prepare reproducible Higher-energy Ps beams using the Ps- ion. A technique to form single-component positron and electron plasmas (the latter for high-quality Ps beams at higher energies is illustrated in Fig. 14 sympathetic antiproton cooling) [62]. [98]. It uses time-compressed pulses of positrons incident upon a Na-coated W foil to create the Ps- ion (i.e., a positron and two As a result of these and other advances, in the last decade electrons). The Ps- is then accelerated and the excess electron antihydrogen trapping rates have increased from 0.1 to 300/h laser stripped. This technique has produced Ps beams with [103]. Figure 15 shows a precision measurement of the 1S – 2S energies from 300 eV to 3 keV and beam divergences of 0.3o. energy transition in antihydrogen [9]. Another recent achievement is the single-photon excitation of the 1S – 2P Alternately, it has been proposed to use a traveling optical lattice (Lyman α) transition in antihydrogen [104]. This sets the stage [99]. Among other applications, such beams offer considerable for laser cooling the antiatoms and further increases in the promise in studying material surfaces. precision of comparisons of the properties of antihydrogen and

hydrogen. To-date, these comparisons have found no differences VI. APPLICATIONS ENABLED BY TRAPS AND TRAP- between the two. A current goal is to study the 1S – 2S transition BASED BEAMS with a precision comparable to that of hydrogen, which will

require an increase in precision of approximately 103s. We review here recent progress in key antimatter applications enabled by the plasma and trap-based tools discussed above and

Fig. 13. Transmission and focusing of a high-Rydberg-state Ps beam [105]. Stark Ps states are formed using a UV and an IR laser. They are reflected from a specially prepared “Rydberg mirror” consisting of closely spaced rods approximately parallel to the beamline with alternating DC potentials that create a localized electric field near the surface. The mirror has a slight curvature such that low-field seeking Ps states are focused on a detector 6 m from the Ps source. See Ref. [105] for further details.

B. Cyclotron resonance magnetometry Because antimatter traps are frequently in a UHV, cryogenic Many of the experiments that can be done with antimatter require environment and have poor access, conventional magnetometry precise knowledge of the local magnetic field. For example, in techniques employing NMR or Hall effect sensors are often experiments intended to measure gravity with antihydrogen atoms, infeasible. In this case, one is led to consider electron cyclotron a magnetic gradient of ~1.8 mT/m will produce a force on the resonance (ECR) magnetometry [106]. This technique uses antiatom equal to the force of gravity. Thus, a 1% accuracy free- variable-frequency microwaves to heat a plasma. From the fall experiment over a range of 0.3 m in a 1 T background field must frequency that maximizes the heating, as determined by the post- control the field strength to the 10 ppm level. illumination plasma temperature, one can calculate the local

9 magnetic field assuming the frequency is the plasma cyclotron It has enabled state-resolved measurements of the positron-impact frequency [107]. cross sections for electronic excitation in atoms and molecules and vibrational excitation of molecules [5]. It has also led to the Recently, two advances have led to ECR measurements at the 1 discovery and study of vibrational Feshbach resonances in positron ppm level [108]. The first advance is the development of a annihilation in molecules, discovery and study of positron-molecule technique to rapidly generate small electron plasmas. An extension bound states, and measurement of positron-molecule binding of work to generate positron pulses [109], pulses from a reservoir energies for a wide variety of molecules [6].2 Another interesting of electron plasma are recaptured to form a succession of ECR area for study is positron-induced fragmentation, which depends target plasmas. These small target plasmas are required to measure critically on the incident positron energy [110, 111]. The fact that the local field in the presence of magnetic gradients. Rapidly positrons with energies close to the threshold for Ps formation generated target plasmas are required to quickly complete a produce little or no fragmentation has potentially important frequency scan, since the target plasma temperature is measured practical consequences [112]. The quest for colder beams to destructively (Sec. IV. A). The second advance is a methodology to improve the energy resolution of such measurements is ongoing. At reliably identify the cyclotron-frequency-resonance peak in the the current level of energy resolution (< 10 meV), maintaining this presence of many other heating resonances. This is accomplished energy resolution downstream of the trap has proven to be by searching for the peak that does not move when the plasma challenging. This must be addressed. electron bounce frequency is scanned. Research on this potentially important technique is ongoing.

Fig. 15. A measurement of the antihydrogen two-photon 1S–2S transition is shown here corresponding to a relative precision of 2 x 10-12 [9]. The points show the number atoms that are detected (appearance) when “kicked” out of the system after illumination by light at various detuning frequencies, and the number of atoms that are missing (disappearance) after illumination as inferred by subtracting the number remaining after illumination from the number before illumination (done with multiple, repeated ensembles.) The line is the result of a simulation with 1W of laser power.

Fig. 14. Formation of a variable-energy Ps beam using Ps- ions [98]. Electrostatic (as opposed to magnetically guided) beams have (above) Schematic diagram of the apparatus. A pulsed positron advantages, particularly in measuring angularly resolved scattering beam from a BGT is focused on a Na coated W film, which emits cross sections. Techniques exist to tailor positron pulses and then Ps- ions. The ions are accelerated through an imposed potential drop extract them from the magnetic field to create electrostatic beams V and then laser stripped to form the Ps beam. (below) Time-of- that can be used for this purpose, however they have yet to be fully flight energy spectra of the resulting beam upon varying V from 0.3 exploited. to 3.5 kV. Study of positron interactions with clusters has been discussed as a C. Positron and positronium interactions with atoms, molecules and fruitful area for investigation [6] (e.g., positronic “cage states” in atomic clusters C60 clusters [113]). Qualitatively, clusters should behave as large molecules. Thus, they should exhibit resonant attachment and The method described in Sec. V to produce pulsed, magnetically bound states, greatly enhancing annihilation rates and providing guided beams with narrow energy spreads has been exploited information about the target. Positron-induced Auger emission extensively for both positron scattering and annihilation studies [5]. could give information about cluster surfaces [114]. However, thus

2 While it is predicted that positrons bind to many atoms, the lack of low-lying excitations in atoms has, to date, hindered study of this process.

10 far, there have been no experiments with clusters, and so this is an F. Electron-positron plasmas interesting area for future investigation. Another many-body electron-positron state, shown in Fig. 16, is the Positronium atoms couple differently to matter than do electrons or classical “pair” plasma, where the Debye length is small compared positrons, and so they give unique information [115]. The new to the dimensions of the charge cloud and > 1, where is the generation of positronium beams can potentially shed light on Ps Debye length. Such a plasma has long been3 predicted to have interactions with atoms and molecules, which is a subject of current distinctly different properties than conventional𝑛𝑛𝜆𝜆𝐷𝐷 electron𝜆𝜆𝐷𝐷 -ion interest [116]. plasmas [123] but has yet to be studied in the laboratory. It has been proposed to confine such a plasma in variety of traps, including a D. Positron studies in condensed matter and materials physics stellarator, levitated magnetic dipole, magnetic mirror and a Penning-Paul trap [20-22, 124, 125]. Research on creating a pair Trap-based beams offer many advantages for research in this area, plasma is currently underway. As part of this effort, preliminary but also have yet to be fully exploited [117, 118]. In the case of experiments using a permanent magnet to mimic a dipole field have positrons, advantages include the possibility of single-shot demonstrated the efficient loading of small numbers of positrons positron-annihilation-lifetime spectroscopy (PALS) [87], pulsed using E x B plates [126] and single-particle positron orbits with beams for enhanced signal to noise in positron-induced Auger lifetimes > 1 s [127]. electron spectroscopy, and rotating-wall radial plasma compression and centerline beam extraction for spatial focusing (e.g., a positron microscope). While useful with all types of positron sources, this might be particularly beneficial at a high-flux reactor or LINAC- based positron beam facility [114].

The new generation of positronium beams offers many important avenues for future investigation of condensed matter phenomena. This arises from the fact that the Ps atom is qualitatively different (i.e., light, uncharged) probe particle, as compared with electrons, positrons or neutral atoms (e.g., He atom diffraction). The use of metal-organic framework (MOF) materials to create nearly monochromatic Ps beams [119], and the technique to create high- Rydberg-state atoms, offer complementary tools with which to conduct a variety of surface analysis experiments. A longstanding goal in this area is to study surfaces using Ps-atom diffraction [120]. The Ps beam described in Ref. [98] is an important step toward this goal. Another goal is to test the quantum reflection of Ps atoms from Fig. 16. Schematic (only) phase diagram of the electron-positron solid surfaces [121]. system as a function of density and temperature . The density nMI of the metal-insulator transition is indicated. While this E. Bose-condensed gases of positronium atoms (Ps BEC) quantum phase is beyond current𝑛𝑛 technology, Ps2 has𝑇𝑇 been created and studied, and near-term studies of a Ps BEC and a classical pair Shown in Fig. 16 is a schematic view of the phase diagram for the plasma are possible. (Adapted from Ref. [128].) many-electron, many-positron system. One fascinating possibility is to create a Ps-atom BEC. Bose condensation requires high densities of cold Ps atoms, which can potentially be achieved by A key impediment to creating a pair plasma is the difficulty in implanting several-keV, partially spin-polarized positrons from a accumulating sufficiently large numbers of positrons (e.g., 1010 – 22Na source into a material with a cavity below the surface [122]. 1012), to be injected in a burst to enter the plasma regime. The The positrons will cool, pick up electrons to become Ps atoms and confinement of such large numbers of particles in a conventional diffuse into the cavity. After the two-gamma decays, the remaining PM trap results in large space charge potentials and hence requires atoms will be in long-lived S =1 states. If they are sufficiently cold large confinement voltages. An alternative positron accumulation and dense, they will transition to the BEC state [3]. The light mass scheme, the so-called multicell trap, has been proposed to of the Ps atoms lowers the requirements on and to achieve the circumvent this impediment [81]. BEC relative to that for ordinary neutral atoms. For example, for a 19 -3 Ps density of 10 cm , the transition temperature𝑛𝑛 is𝑇𝑇 c= 90 K. VII. KEY TOPICS FOR FUTURE RESEARCH

Experiments are in progress to achieve such a state. They𝑇𝑇 employ a Much progress has been made in trapping antimatter, tailoring the BGT and accumulator with a RW, buncher and pulsed magnetic resulting plasma, and then tailoring delivery with specific field to create bursts of ~ 108 positrons, which will then be extracted applications in mind. The successes, and in some cases, the lack of from the magnetic field and electrostatically metal remoderator to progress raises new opportunities and necessities for further further increase beam emittance ( / , where is the research. Here we give some examples. beam energy and D the diameter, and is the spread in transverse ⊥ 0 0 Improved plasma compression. The rotating wall technique has energies). It is planned that the beam𝜖𝜖 would ≡𝐷𝐷�Δ𝐸𝐸 then𝐸𝐸 be accelerated𝐸𝐸 and ⊥ proven to be a key tool in working with both positrons and refocused on a suitable material to formΔ𝐸𝐸 a dense Ps focused on a gas antiprotons. As discussed in Sec. IV. B, this technique can be used and a Ps BEC [3]. to approach within a factor of six or less of the Brillouin (the

11 maximum possible) density limit when operated at 0.04 T and using ALPHAg scheme. Moreover, the current ECR schemes only buffer-gas cooling. At higher magnetic fields, while the absolute measures the on-axis field. The extension of this technique to the density reached is somewhat larger, it is nowhere near the Brillouin measurement of off-axis fields would be very useful. limit, particularly at tesla-strength fields where one relies on cyclotron cooling. This limiting behavior is not currently Higher quality positronium-atom beams. Much progress has been understood. Given the importance of large antiparticle densities for made in creating high quality Ps beams, and ones with long-lived many applications, this should be a priority for further investigation. high-Rydberg-state atoms. That said, the particle fluxes achieved to date are quite small. This area is in its infancy, and one can likely Colder positron gases and plasmas. Techniques to prepare clouds expect future improvements in technique. of colder positrons could be very useful. This might be accomplished using the resonant cavity cooling technique described Spin polarized positrons. Spin polarized positrons would be useful above. Sympathetic cooling with laser-cooled ions might be another in a number of applications. This raises the question as to whether useful approach. techniques can be developed to spin-polarize trapped positrons from an unpolarized source such as the NEPOMUC beam at the Improved positron/antiproton mixing. The techniques to mix Technical University of Munich [138] or increase the degree of positron and antiproton plasmas to create antihydrogen are poorly polarization of positrons from a radioisotope source such as 22Na. understood and are thus tuned empirically. Simulations which One possibility is to put a PM trap in a magnetic field gradient and properly model the process might be informative. These extract positrons from one end. Unfortunately, one would need simulations will need to model both the antiproton and positron plasmas colder than 1 K to do this, which is at present very dynamics, include radial spatial effects as well as all three challenging. momentum dimensions and properly model collisions. Ideally, the simulations would model the exact procedures used in the various Larger numbers of positrons. Creation of a pair plasma is an experiments, including the details of antiproton injection and any application where large numbers of positrons are required (e.g., simultaneous adiabatic expansion/evaporative/sympathetic ~ 1010 - 1012). The practical capacity of a single PM trap is made cooling. They would be particularly useful if they were able to difficult by space charge. The larger the number of particles𝑁𝑁 provide insights into improving the antihydrogen formation and confined, the larger the space charge potential and hence the larger trapping fraction [129-132]. the required confining potential. One could work with a single plasma with a very large confining potential, but it is thought that Sympathetic cooling of positively charged antihydrogen atoms. The the large space charge may well result in electrical breakdown GBAR collaboration intends to prepare the atoms for an and/or unacceptable levels of expansion heating. As an alternative, antihydrogen fountain using an intermediate step of the possibility of using a multicell trap with an array of PM traps sympathetically-cooled, positively-charged antihydrogen ions arranged in parallel in a common vacuum and magnetic field is [133]. These anti-ions are the antimatter analog of negatively being pursued [81]. charged hydrogen ions. Both the generation and sympathetic cooling of these anti-ions will require further research. Portable antimatter traps. A portable trap with capacity ~ 1012 would be of interest for a variety of positron applications. For Antihydrogen beams. The antihydrogen physics results to date have example, such a trap would useful at a location (a synchrotron𝑁𝑁 or been obtained with trapped antiatoms. There are potential physics chip assembly line) where a separate positron source is undesirable. advantages to working with antihydrogen beams; primarily the Such a trap is, in principal, possible (e.g., using a multicell trap). transport of the antihydrogen out of the strong magnet field However, present superconductor magnets require low environment necessary for the synthesis of antihydrogen. Weak temperatures, and this is a key impediment. Thus, such a trap beams, not yet necessarily in the required ground state, have been appears to hinge on the further development in magnet technology created by the ASACUSA collaboration for hyperfine studies [134], (i.e., high-Tc superconductors). and the AEGIS collaboration is attempting to make beams for gravity studies [135]. In parallel with work on the positron transport, the PUMA project at CERN [139] intends to capture and transport, by truck, 109 Handling more antiprotons and the creation of antideuterium. With antiprotons from CERN’s AD to their ISOLDE facility [140]. At the coming operation of CERN’s ELENA ring, orders of magnitude ISOLDE, interactions between the antiprotons and exotic nuclei more antiprotons are expected to be available [17]. Efficiently will be investigated. The BASE collaboration is considering utilizing the additional antiprotons presents new challenges to transporting ~ 100 antiprotons out of the AD hall to a quieter mixing schemes. Conversely, with the capability of producing environment to facilitate their measurements [141]. antideuterons at Brookhaven National Laboratory comes the possibility, albeit very challenging, of creating antideuterium [136]. VIII. CONCLUDING REMARKS Since vastly fewer antideuterons than antiprotons would be available, new positron/antideuteron mixing schemes with far more Science with antimatter at low energies (e.g., tens of electron volts efficient utilization of the antideuterons will need to be developed. or less) is a relatively new area of investigation but one in which there has been much progress and one that offers considerable Improved electron cyclotron resonance magnetometry. While ECR potential for future science and technology. This article focuses on magnetometry has been perfected to the 1 ppm level, it is not yet the ways in which plasma techniques have played a central role in clear that it will be useable in the strong magnetic field gradients in this research and a glimpse as to what the future might hold for the ALPHAg antihydrogen experiment [137], especially as the further progress. ALPHAg magnets are ramped, which is an intrinsic part of the

12 The capabilities to trap and cool positrons and antiprotons has [10] M. Ahmadi, et al., Observation of the Hyperfine Spectrum of increased dramatically since the first efforts in the 1980s. Numerous Antihydrogen, Nature 548, 66 (2017). new techniques have been developed to create ever more dense and [11] M. Pospelov, Breaking of CPT and Lorentz Symmetries, Hyperfine cold antiparticle gases and plasmas and to manipulate them in novel Int. 172, 63 (2006). [12] C. Amole, et al., Description and First Application of a New ways. Similarly, techniques have been developed for antiparticle Technique to Measure the Gravitational Mass of Antihydrogen, delivery, frequently as specially tailored beams. Of particular note Nature Communications 4, 1785 (2013). is the recent success in matching clouds of antiparticles to laser [13] G. Gabrielse, et al., Thousandfold Improvement in the Measured radiation for further manipulation, and/or precision experiments. Antiproton Mass, Phys. Rev. Lett. 65, 1317 (1990). [14] C. Smorra, et al., A Parts-Per-Billion Measurement of the These techniques have provided qualitatively new scientific Antiproton Magnetic Moment, Nature Letters 550, 371 (2017). insights and technological capabilities. The trapping and cooling of [15] J. R. Danielson, D. H. E. Dubin, R. G. Greaves, and C. M. Surko, antiprotons, positrons and electrons enabled the first successful Plasma and Trap-Based Techniques for Science with Positrons, Rev. Mod. Phys. 87, 247 (2015). formation of low-energy antihydrogen atoms, and improvements in [16] S. Maury, The Antiproton Decelerator: Ad, Hyperfine Inter. 109, 43 the plasma techniques have led to an increase in the antihydrogen (1997). trapping rate by more than a factor of 1000 in the last decade. These [17] W. Bartmann, et al., The Elena Facility, Phil. Trans. Royal Soc. A techniques also led to similar progress in understanding and 376, 20170266 (2018). exploiting positron-matter interactions. Examples include the [18] C. M. Surko, A. Passner, M. Leventhal, and F. J. Wysocki, Bound creation and study of the positronium molecule (di-positronium, States of Positrons and Large Molecules, Phys. Rev. Lett. 61, 1831 (1988). Ps2), positron binding to molecules and atoms, and high-quality beams of positronium atoms. [19] C. M. Surko, M. Leventhal, and A. Passner, Positron Plasma in the Laboratory, Phys. Rev. Lett. 62, 901 (1989). [20] H. Boehmer, M. Adams, and N. Rynn, Positron Trapping in a The future of progress in this area is exceedingly bright. This is in Magnetic Mirror Configuration, Phys. Plasmas 2, 4369 (1995). no small part because of increased understanding of the importance [21] H. Higaki, et al., Simultaneous Confinement of Low-Energy of plasma techniques in the atomic physics, fundamental physics, Electrons and Positrons in a Compact Magnetic Mirror Trap, N. J. and condensed matter physics communities, and the increased Phys. 19, 023016 (2017). appreciation in the plasma community of problems and [22] H. Saitoh, et al., Stable Confinement of Electron Plasma and Intital opportunities in these areas. Results on Positron Injection in Rt-1, in Non-Neutral Plasma Physics Viii (AIP Conference Proceedings, Melville, NY, 2013), Vol. 1521, p. 63. ACKNOWLEDGEMENTS [23] J. H. Malmberg and J. S. DeGrassie, Properties of Nonneutral Plasma, Phys. Rev. Lett. 35, 577 (1975). We wish to acknowledge helpful conversations with W. Bertsche, [24] T. M. O'Neil, A Confinement Theorem for Nonneutral Plasmas, D. Cassidy, M. Charlton, J. Danielson, R. Greaves, A. Mills, Y. Phys. of Fluids 23, 2216 (1980). Nagashima, and D. van der Werf and a careful reading of the [25] C. F. Driscoll, J. H. Malmberg, and K. S. Fine, Observation of manuscript by F. Anderegg, W. Bertsche, M. Charlton, E. Gilson, Transport to Thermal Equilibrium in Pure Electron Plasmas, J. Danielson and K. Zukor. This work has been supported by the U. Physical Review Letters 60, 1290 (1988). S. DOE grants DE0016532, DE-SC0019271, and DE-SC0019346, [26] D. H. E. Dubin and T. M. O'Neil, Trapped Nonneutral Plasmas, Liquids, and Crystals (the Thermal Equilibrium States), Rev. Mod. and NSF grants PHY1702230 and PHY1806305. Phys. 71, 87 (1999). [27] C. F. Driscoll and J. H. Malmberg, Length-Dependent Containment REFERENCES of a Pure Electron-Plasma Column, Phys. Rev. Lett. 50, 167 (1983). [28] A. Christensen, private communication (2019). [1] P. J. Schultz and K. G. Lynn, Interaction of Positrons Beams with [29] M. R. Natisin, J. R. Danielson, and C. M. Surko, A Cryogenically Surfaces, Thin Films, and Interfaces, Rev. Mod. Phys. 60, 701 Cooled, Ultra-High-Energy-Resolution, Trap-Based Positron Beam, (1988). Appl. Phys. Lett. 108, 024102 (2016). [2] R. L. Wahl, Principles and Practice of Positron Emission [30] T. Mohamed, A. Mohri, and Y. Yamazaki, Comparison of Non- Tomography, in Principles and Practice of Positron Emission Neutral Electron Plasma Confinement in Harmonic and Rectangular Tomography (Lippincott, Williams and Wilkins, Philadelphia, PA, Potentials in a Very Dense Regime, Phys. Plasmas 20, 012502 2002). (2013). [3] A. P. Mills, Possible Experiments with High Density Positronium, [31] C. M. Surko, R. G. Greaves, and M. Charlton, Stored Positrons for AIP Conf. Proc. 2182, 030001 (2019). Antihydrogen Production, Hyperfine Interactions 109, 181 (1997). [4] D. B. Cassidy, T. H. Hisakado, H. W. K. Tom, and A. P. J. Mills, [32] S. Sellner, et al., Improved Limit on the Directly Measured Optical Spectroscopy of Molecular Positronium, Phys. Rev. Lett. Antiproton Lifetime, New J. Phys. 19, 083023 (2017). 108, 133402 (2012). [33] J. R. Danielson and C. M. Surko, Radial Compression and Torque- [5] C. M. Surko, G. F. Gribakin, and S. J. Buckman, Low-Energy Balanced Steady States of Single-Component Plasmas in Penning- Positron Interactions with Atoms and Molecules, J. Phys. B: At. Malmberg Traps, Phys. Plasmas 13, 055706 (2006). Mol. Opt. Phys. 38, R57 (2005). [34] R. G. Greaves and C. M. Surko, Solid Neon Moderator for Positron [6] G. F. Gribakin, J. A. Young, and C. M. Surko, Positron-Molecule Trapping Experiments, Can. J. Phys. 51, 445 (1996). Interactions: Resonant Attachment, Annihilation, and Bound States, [35] A. P. Mills and E. M. Gullikson, Solid Neon Moderator for Rev. Mod. Phys. 82, 2557 (2010). Producing Slow Positrons, Appl. Phys. Lett. 49, 1121 (1986). [7] A. P. Mills and M. Leventhal, Can We Measure the Gravitational [36] A. P. Mills, Further Improvements in the Efficiency of Low-Energy Free Fall of Cold {R}Ydberg State Positronium?, Nuc. Instrum. Positron Moderators, Appl. Phys. Lett. 37, 667 (1980). Meth. B 192, 102 (2002). [37] E. V. Stenson, U. Hergenhahn, M. R. Stoneking, and T. S. [8] D. B. Cassidy, Experimental Progress in Positronium Laser Physics, Pedersen, Positron-Indeuced Luminescence, Phys. Rev. Lett. 120, Euro. Phys. J. D 72, 53 (2018). 147401 (2018). [9] M. Ahmadi, et al., Characterization of the 1s-2s Transition in Antihydrogen, Nature Letters 557, 71 (2018).

13 [38] G. B. Andresen, et al., Antiproton, Positron, and Electron Imaging [63] G. B. Andresen, et al., Evaporative Cooling of Antiprotons to with a Microchannel Plate/Phosphor Detector, Rev. Sci. Instrum. Cryogenic Temperatures, Phys. Rev. Lett. 105, 013003 (2010). 80, 123701 (2009). [64] G. Gabrielse, et al., Adiabatic Cooling of Antiprotons, Phys. Rev. [39] A. J. Peurrung and J. Fajans, A Pulsed Microchannel-Plate-Based Lett. 106, 073002 (2011). Non-Neutral Plasma Imaging System, Rev. Sci. Instrum. 64, 52 [65] X. P. Huang, et al., Precise Control of the Global Rotation of (1993). Strongly Coupled Ion Plasmas in a Penning Trap, Phys. Plasmas 5, [40] R. L. Spencer, S. N. Rasband, and R. R. Vanfleet, Numerical- 1656 (1998). Calculation of Axisymmetrical Nonneutral Plasma Equilibria, Phys. [66] F. Anderegg, E. M. Hollmann, and C. F. Driscoll, Rotating Field Fluids B 5, 4267 (1993). Confinement of Pure Electron Plasmas Using Trivelpiece-Gould [41] D. H. E. Dubin, Theory of Electrostatic Fluid Modes in a Cold Modes, Phys. Rev. Lett. 81, 4875 (1998). Spheroidal Non-Neutral Plasma, Phys. Rev. Lett. 66, 2076 (1991). [67] X. P. Huang, F. Anderegg, E. M. Hollmann, C. F. Driscoll, and T. [42] M. D. Tinkle, R. G. Greaves, and C. M. Surko, Low-Order M. O'Neil, Steady State Confinement of Nonneutral Plasma by Longitudinal Modes of Single-Component Plasmas, Phys. of Rotating Electric Fields, Phys. Rev. Lett. 78, 875 (1997). Plasmas 2, 2880 (1995). [68] R. G. Greaves and C. M. Surko, Radial Compression and Inward [43] D. L. Eggleston, C. F. Driscoll, B. R. Beck, A. W. Hyatt, and J. H. Transport of Positron Plasmas Using a Rotating Electric Field, Malmberg, Parallel Energy Analyzer for Pure Electron Plasma Phys. Plasmas 8, 1879 (2001). Devices, Phys. Fluids B 4, 3432 (1992). [69] R. G. Greaves and J. M. Moxom, Compression of Trapped [44] T. Hsu and J. L. Hirshfield, Electrostatic Energy Analyzer Using a Positrons in a Single Particle Regime by a Rotating Electric Field, Nonuniform Axial Magnetic Field, Rev. Sci. Instrum. 47, 236 Phys. Plasmas 15, 072304 (2008). (1976). [70] C. A. Isaac, C. J. Baker, T. Mortensen, D. P. v. d. Werf, and M. [45] A. W. Hyatt, C. F. Driscoll, and J. H. Malmberg, Measurement of Charlton, Compression of Positron Clouds in the Independent the Anisotropic Temperature Relaxation Rate in a Pure Electron Particle Regime Phys. Rev. Lett. 107, 033201 (2011). Plasma, Phys. Rev. Lett. 59, 2975 (1987). [71] G. B. Andresen, et al., Compression of Antiproton Clouds for [46] M. D. Tinkle, R. G. Greaves, C. M. Surko, R. L. Spencer, and G. Antihydrogen Trapping Phys. Rev. Lett. 100, 203401 (2008). W. Mason, Low-Order Modes as Diagnostics of Spheroidal Non- [72] N. Kuroda, et al., Radial Compression of an Antiproton Cloud for Neutral Plasmas, Phys. Rev. Lett. 72, 352 (1994). Production of Intense Antiproton Beams, Phys. Rev. Lett. 100, [47] M. Amoretti, et al., Positron Plasma Diagnostics and Temperature 203402 (2008). Control for Antihydrogen Production, Phys. Rev. Lett. 91, 055001 [73] J. R. Danielson, C. M. Surko, and T. M. O'Neil, High-Density (2003). Fixed Point for Radially Compressed Single-Component Plasmas, [48] M. Amoretti, et al., Complete Nondestructive Diagnostic of Phys. Rev. Lett. 99, 135005 (2007). Nonneutral Plasmas Based on the Detection of Electrostatic Modes, [74] R. C. Davidson, Physics of Nonneutral Plasmas, in Physics of Phys. Plasmas 10, 3056 (2003). Nonneutral Plasmas (Addison-Wesley, Reading, MA, 1990). [49] T. R. Weber, J. R. Danielson, and C. M. Surko, Creation of Finely [75] C. M. Surko, J. R. Danielson, and T. R. Weber, Accumulation, Focused Particle Beams from Single-Component Plasmas, Phys. Storage and Manipulation of Large Numbers of Positrons in Traps Plasmas 13, 123502 (2008). II: Selected Topics, in Physics with Trapped Charged Particles, [50] N. Shiga, F. Anderegg, D. H. E. Dubin, C. F. Driscoll, and R. W. edited by M. Kroop, N. Madsen and R. C. Thompson (Imperial Gould, Thermally Excited Fluctuations as a Pure Electron Plasma College Press, London, U. K., 2014), p. 129. Temperature Diagnostic Phys. Plasmas 13, 022109 (2006). [76] J. R. Danielson and C. M. Surko, Torque-Balanced High-Density [51] T. J. Murphy and C. M. Surko, Positron Trapping in an Electrostatic Steady States of Single Component Plasmas, Phys. Rev. Lett. 94, Well by Inelastic Collisions with Nitrogen Molecules, Phys. Rev. A 035001 (2005). 46, 5696 (1992). [77] S. Aghion, et al., Compression of a Mixed Antiproton and Electron [52] M. R. Natisin, J. R. Danielson, and C. M. Surko, Positron Cooling Non-Neutral Plasma to High Densities, Euro. Phys. J. D 72, 76 by Vibrational and Rotational Excitation of Molecular Gases, J. (2018). Phys. B 47, 225209 (2014). [78] J. Fajans and L. Friedland, Autoresonant (Non Stationary) [53] T. M. O'Neil, Cooling of a Pure Electron Plasma by Cyclotron Excitation of a Pendulum, Plutinos, Plasmas and Other Nonlinear Radiation, Phys. Fluids 23, 725 (1980). Oscillators, Am. J. Phys. 69, 1096 (2001). [54] J. H. Malmberg, et al., Experiments with Pure Electron Plasmas, in [79] G. B. Andresen, et al., Autoresonant Excitation of Antiproton Non-Neutral Plasma Physics, edited by C. W. Roberson and C. F. Plasmas, Phys. Rev. Lett. 106, 025002 (2011). Driscoll (American Institute of Physics, New York, 1988), p. 28. [80] J. R. Danielson, T. R. Weber, and C. M. Surko, Plasma [55] M. E. Glinsky, T. M. O. Neil, M. N. Rosenbluth, K. Tsuruta, and S. Manipulation Techniques for Positron Storage, Phys. Plasmas 13, Ichimaru, Collisional Equipartition Rate for a Magnetized Pure 123502 (2006). Electron Plasma, Physics of Fluids B 4, 1156 (1992). [81] N. C. Hurst, J. R. Danielson, C. J. Baker, and C. M. Surko, [56] E. D. Hunter, et al., Low Magnetic Field Cooling of Lepton Confinement and Manipulation of Electron Plasmas in a Multicell Plasmas Via Cyclotron-Cavity Resonance, Phys. Plasmas 25, Trap, Phys. Plasmas 26, 013513 (2019). 011602 (2018). [82] M. Ahmadi, et al., Antihydrogen Accumulation for Fundamental [57] E. M. Purcell, Spontaneous Emission Probabilities at Radio Symmetry Tests, Nature Communications 8, 681 (2017). Frequencies, Proc. Am. Phys. Soc. 69, 681 (1946). [83] L. V. Jorgensen, et al., New Source of Dense, Cryogenic Positron [58] G. Gabrielse, et al., First Capture of Antiprotons in a Penning Trap: Plasmas, Phys. Rev. Lett. 95, 025002 (2005). A Kiloelectronvolt Source, Phys. Rev. Lett. 57, 2504 (1986). [84] D. W. Fitzakerley, et al., Electron Cooling and Accumulation of 4 x [59] G. Gabrielse, et al., Cooling and Slowing of Trapped Antiprotons 109 Positrons in a System for Longterm Storage of Antihydrogen Below 100 MeV, Phys. Rev. Lett. 63, 1360 (1989). Atoms, Bull. Am. Phys. Soc. 58, 176 (2013). [60] B. M. Jelenkovic, A. S. Newbury, J. J. Bollinger, W. M. Itano, and [85] M. R. Natisin, J. R. Danielson, and C. M. Surko, Formation T. B. Mitchell, Sympathetically Cooled and Compressed Positron Mechanisms and Optimization of Trap-Based Beams, Phys. Plasma, Phys. Rev. A 67, 063406 (2003). Plasmas 23, 023505 (2016). [61] N. Madsen, S. Jonsell, and F. Robicheaux, Antihydrogen Trapping [86] D. B. Cassidy, et al., Experiments with a High-Density Positronium Assisted by Sympathetically Cooled Positrons, New J. Phys. 16, Gas, Phys. Rev. Lett. 95, 195006 (2005). 063046 (2014). [87] D. B. Cassidy, S. H. M. Deng, H. K. M. Tanaka, and A. P. Mills, [62] M. Ahmadi, et al., Enhanced Control and Reproducibility of Non- Single Shot Positron Annihilation Lifetime Spectroscopy, Appl. Neutral Plasmas, Phys. Rev. Lett. 120, 025001 (2018). Phys. Lett. 88, 194105 (2006).

14 [88] M. Maekawa and A. Kawasuso, Development of Pulsed Positron [113] F. A. Gianturco and R. R. Lucchese, Computational Investigation of Beam Line with Compact Pulsing System, Nucl. Instrum. Meth. B Positron Scattering from C60, Phys. Rev. A 60, 4567 (1999). 270, 23 (2012). [114] C. Hugenschmidt, Positrons in Surface Physics, Surf. Sci. Reports [89] R. G. Greaves and C. M. Surko, Positron Trapping and the Creation 71, 547 (2016). of High-Quality Trap-Based Positron Beams, Nucl. Instrum. [115] G. Laricchia and H. R. J. Walters, Positronium Collision Physics, Methods B 192, 90 (2002). Rivista del Nuovo Cimento 35, 305 (2012). [90] W. Stoeffl, P. Asoka-Kumar, and R. Howell, The Positron [116] I. I. Fabrikant, G. F. Gribakin, and R. S. Wilde, Positronium Microprobe at Lawrence Livermore National Laboratory, Appl. Collisions with Atoms and Molecules, Journal of Physics Conferece Surf. Sci. 149, 1 (1999). Series 875, 012001 (2017). [91] A. P. Mills, Brightness Enhancement of Slow Positron Beams, [117] C. Hugenschmidt, Present and Future Experiments Using Bright Appl. Phys. 23, 189 (1980). Low-Energy Positron Beams, J. Phys. B: Conf. Series 791, 012002 [92] D. B. Cassidy, S. H. M. Deng, R. G. Greaves, and A. P. Mills, (2017). Accumulator for the Production of Intense Positron Pulses, Rev. [118] D. Chaudhary, M. R. Went, K. Nakagawa, S. Buckman, and J. P. Sci. Instrum. 77, 073106 (2006). Sullivan, Molecular Pore Size Characterization within Chitosan [93] D. B. Cassidy, V. E. Meligne, and A. P. Mills, Production of a Fully Biopolymer Using Positron Annihilation Lifetime Spectroscopy, Spin-Polarized Ensemble of Positronium Atoms, Phys. Rev. Lett. Mater. Lett. 64, 2635 (2010). 104, 173401 (2010). [119] A. C. L. Jones, et al., Monoenergetic Positronium Emission from [94] M. Charlton and J. W. Humberston, Positron Physics (Cambridge Metal-Organic Framework Crystals, Phys. Rev. Lett. 114, 153201 Univ. Press, Cambridge, U. K., 2001). (2015). [95] D. B. Cassidy, T. H. Hisakado, H. W. K. Tom, and A. P. Mills, [120] K. F. Canter, Low Energy Positron and Positronium Diffraction., in Efficient Production of Rydberg Positronium, Phys. Rev. Lett. 108, Positron Scattering in Gases, edited by J. W. Humberston and M. 043401 (2012). R. C. McDowell (Plenum, New York, 1983), p. 219. [96] M. Charlton, Antihydrogen Production in Collisions of Antiprotons [121] A. P. Mills, New Experiments with Bright Positron and Positronium with Excited States of Positronium, Physics Letters A 143, 143 Beams, in New Directions in Antimater Chemistry and Physics, (1990). edited by C. M. Surko and F. A. Gianturco (Kluwer Academic, [97] C. H. Storry, et al., First Laser-Controlled Antihydrogen Netherlands, 2001), p. 115. Production, Phys. Rev. Lett. 93, 263401 (2004). [122] A. P. Mills, Positronium Molecule Formation, Bose-Einstein [98] K. Michishio, L. Chiari, F. Tanaka, N. Oshima, and Nagashima, A Condensation and Stimulated Annihilation, Nucl. Instrum. Methods High-Quality and Energy-Tunable Positronium Beam System B 192, 107 (2002). Employing a Trap-Based Positron Beam, Rev. Sci. Instrum. 90, [123] V. Tsytovich and C. B. Wharton, Laboratory Electron-Positron 023305 (2019). Plasma-a New Research Object, Comments Plasma Phys. [99] P. F. Barker and M. Charlton, Directed Fluxes of Positronium Controlled Fusion 4, 91 (1978). Using Pulsed Travelling Optical Lattices, New J. Phys. 045005 [124] T. S. Pedersen, et al., Plans for the Creation and Studies of (2012). Electron–Positron Plasmas in a Stellarator, New J. Phys. 14, [100] M. Amoretti, et al., Production and Detection of Cold Antihydrogen 035010 (2012). Atoms, Nature 419, 456 (2002). [125] C. M. Surko, J. R. Danielson, and T. R. Weber, Accumulation, [101] G. Gabrielse, et al., Driven Production of Cold Antihydrogen and Storage and Manipulation of Large Numbers of Positrons in Traps the First Measured Distribution of Antihydrogen States, Phys. Rev. {Ii}. – Selected Topics, in Physics with Many Positrons, edited by Lett. 89, 233401 (2002). A. P. Mills and A. Dupasquier (IOS press, Amsterdam, 2010), p. [102] G. B. Andresen, et al., Confinement of Antihydrogen for 1,000 545. Seconds, Nature Physics 7, 558 (2011). [126] E. V. Stenson, et al., Lossless Positron Injection into a Magnetic [103] J. S. Hangst, in Spectroscopic and gravitational measurements on Dipole Trap, Phys. Rev. Lett. 121, 235005 (2018). antihydrogen: ALPHA-3, ALPHA-g and beyond, CERN-SPSC- [127] J. Horn-Stanja, et al., Confinement of Positrons Exceeding 1 2019-036 ; SPSC-P-362 (CERN, Geneva Switzerland, 2019). Second in a Supported Magnetic Dipole Trap, Phys. Rev. Lett. 121, [104] M. Ahmadi, et al., Observation of the 1S-2P Lyman-Alpha 235003 (2018). Transition in Antihydrogen, Nature 561, 211 (2018). [128] H. Yabu, Many Positron and Positronium Interactions, Nuc. [105] A. C. L. Jones, et al., Focusing of a Rydberg Positronium Beam Instrum. Meth. B 221, 144 (2004). with an Ellipsoidal Electrostatic Mirror, Phys. Rev. Lett. 119, [129] E. M. Bass and D. H. E. Dubin, Antihydrogen Formation from 053201 (2017). Antiprotons in a Pure Positron Plasma, Phys. Plasmas 16, 012101 [106] C. Amole, et al., In Situ Electromagnetic Field Diagnostics with an (2008). Electron Plasma in a Penning–Malmberg Trap, New J. Phys. 16, [130] F. Robicheaux and J. D. Hanson, Three-Body Recombination for 013037 (2014). Protons Moving in a Strong Magnetic Field, Phys. Rev. A 69, [107] M. Affolter, F. Anderegg, and C. F. Driscoll, Space Charge 010701 (R) (2004). Frequency Shifts of the Cyclotron Modes in Multi-Species Ion [131] F. Robicheaux, Simulations of Antihydrogen Formation, Phys. Rev. Plasmas, J. Am. Soc. Mass Spectrom. 26, 330 (2015). A 70, 022510 (2004). [108] E. D. Hunter, et al., Electron Cyclotron Resonance (Ecr) [132] S. Jonsell and M. Charlton, Formation of Antihydrogen Beams Magnetometry with a Plasma Reservoir, arXiv:1912.04358 (2019). from Positron–Antiproton Interactions, New J. Phys. 21, 073020 [109] J. R. Danielson, T. R. Weber, and C. M. Surko, Extraction of (2019). Small-Diameter Beams from Single-Component Plasmas, Appl. [133] W. Grabowski, Gbar - Principle of the Experiment. Phys. Lett. 90, 081503 (2007). https://gbar.web.cern.ch/GBAR/public/en/principle.html [110] A. Passner, C. M. Surko, M. Leventhal, and A. P. Mills, Ion [134] Y. Enomoto, et al., Synthesis of Cold Antihydrogen in a Cusp Trap, Production by Positron-Molecule Resonances, Phys. Rev. A 39, Phys. Rev. Lett. 105, 243401 (2010). 3706 (1989). [135] A. Kellerbauer, et al., Proposed Antimatter Gravity Measurement [111] L. D. Hulett, J. Xu, S. A. McLuckey, T. A. Lewis, and D. M. with an Antihydrogen Beam, Nucl. Instrum. Meth. B 266, 351 Schrader, The Ionization of Organic Molecules by Slow Positrons, (2008). Can. J. Phys. 74, 411 (1996). [136] J. Adam, et al., Beam Energy Dependence of (Anti-)Deuteron [112] L. D. Hulett, J. Xu, S. A. ÂcLuckey, and D. M. Schrader, The Production in Au + Au Collisions at the Bnl Relativistic Heavy Ion Interaction of Slow Positrons with Organic Molecules above and Collider, Phys. Rev. C 99, 064905 (2019). Below Positronium Formation Thresholds, J. of Radioanal. and [137] A. I. Zhmoginov, A. E. Charman, R. Shalloo, J. Fajans, and J. S. Nucl. Chem. 210, 309 (1996). Wurtele, Nonlinear Dynamics of Anti-Hydrogen in Magnetostatic

15 Traps: Implications for Gravitational Measurements, Class. Quantum Grav. 30, 205014 (2013). [138] C. Hugenschmidt, C. Piochacz, M. Reiner, and K. Schreckenbach, The Nepomuc Upgrade and Advanced Positron Beam Experiments, New J. Phys. 14, 055027 (2012). [139] ELENA doi: 10.1098/rsta.2017.0266 [140] Physicists Plan Antimatter’s First Outing — in a Van, Nature 554, 412 (2018). [141] S. Ulmer, et al., 2019), https://cds.cern.ch/record/002702758.

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